Windows Explorer, on doubleclick on any file, takes about 7 seconds to
launch the associated application, then another 2 seconds to open the
file.

I've checked in task manager, no apps are draining the CPU ressources
when exlorer hangs on the launch. All apps are responding that way.
Opening the context menue with a right-click on a file needs 7 seconds too.

If I start let's say, Word or Excel, the apps load right away.
Then I go in File/Open and open a file. The file opens immediately.

There is a network activity in the app-launching time: LAN Connection status
shows
Activity. 12 packets sent.
If the other network computer is running, time to launch an application is
75 seconds.
It doesn't matter if the Internet Firewall / Symantec Personal Firewall are
activated or not.

However, deactivating the LAN connection results in an immediate launching
the apps.

Thanks for your answer. I run RegScanner, looking for "\\" in HKRC,
but I found no entries pointing to a file/application in the other network
computer. Besides, if the network computer is running, application
launching time is even much longer. Only deactivating the LAN connection
helps.
Here a small section of a RegScanner result (scanning for "shell\open").
Entries for other apps are of the same pattern.
....
HKCR\Word.Backup.8\shell\Open REG_SZ Ã½&ffnen
HKCR\Word.Backup.8\shell\Open\command REG_SZ "C:\Programme\Microsoft
Office\Office10\WINWORD.EXE" /n /dde
HKCR\Word.Backup.8\shell\Open\command command REG_MULTI_SZ
&f'^Vn-}f(YR]eAR6.jiWORDFiles>L&rfUmW.cG.e%fI4G}jd /n /dde;;
HKCR\Word.Backup.8\shell\Open\ddeexec REG_SZ [REM
_DDE_Direct][FileOpen("%1")]
HKCR\Word.Backup.8\shell\Open\ddeexec\Application REG_SZ WinWord
HKCR\Word.Backup.8\shell\Open\ddeexec\Topic REG_SZ System
HKCR\Word.Document.8\shell\Open REG_SZ Ã½&ffnen
HKCR\Word.Document.8\shell\Open\command REG_SZ "C:\Programme\Microsoft
Office\Office10\WINWORD.EXE" /n /dde
HKCR\Word.Document.8\shell\Open\command command REG_MULTI_SZ
&f'^Vn-}f(YR]eAR6.jiWORDFiles>L&rfUmW.cG.e%fI4G}jd /n /dde;;
HKCR\Word.Document.8\shell\Open\ddeexec REG_SZ [REM
_DDE_Direct][FileOpen("%1")]
HKCR\Word.Document.8\shell\Open\ddeexec\Application REG_SZ WinWord
HKCR\Word.Document.8\shell\Open\ddeexec\Topic REG_SZ System
HKCR\Word.RTF.8\shell\Open REG_SZ Ã½&ffnen
....

My applications are installed in C:\Programme\, and the registry entries
seem correct to me.
I don't understand why the explorer seems to look for the associated
application in another place, The launching problem occcurs on
doubleclicking any file, not
just with a specific application.

You solved my explorer problem! Applications are opened without delay
on doubleclick, the context menus unfold immediately.

I scanned HKCU for "\\" with RegScanner. I found some entries
pointing to a network computer, one of them indicating an application
KOOLMOVES. I deinstalled Koolmoves and erased remaining Koolmoves
registry entries.